The purpose of this proposal is to address the statistical issues related to and to develop statistical methods for the analysis of interval-censored data arising from AIDS studies. Such studies play an essential role in AIDS treatment development, the understanding of AIDS epidemic and the process of health-related policy-making. AIDS clinical trial is a key component of the development of AIDS treatments and the interval-censoring problem frequently occurs in this situation. In practice, the interval-censoring problem is usually simplified due to the unavailability of the appropriate statistical methods. A major component of the proposed research involves developing statistical methods that take into account the interval-censoring structure of the data and are appropriate for the analysis of AIDS clinical trials. AIDS cohort follow-up studies are commonly used to obtain the knowledge about AIDS incubation time, which is important in understanding both the process of AIDS disease and HIV and AIDS epidemics. In this case, the interval-censoring occurs more often and has a much more complicated structure than in the case of AIDS clinical trials. The proposed research will assess and develop existing and new statistical methods, respectively, for inference about AIDS incubation time based on interval-censored data. It will also develop guidelines for more efficient and precise estimation of the distribution of AIDS incubation time. The analysis of AIDS surveillance data is constantly conducted in order to monitor HIV and AIDS epidemics and provide essential information to the US Government to make health-related policies. In this situation, the analysis must address both interval- censoring and reporting delay problems simultaneously. One component of the proposed research concerns the development of a simple and practical statistical method for inference about AIDS survival time based on AIDS surveillance data and the guidelines for more accurate estimation of HIV prevalences and projections of future AIDS incidences.